One way to save money is to meticulously seal out moisture from the basement. I don't have a basement here, but I have my crawl space so well sealed, the pipes don't gather condensate in the summer. I have the floor covered with plastic going up the walls, the block walls cover with cement based paint, and the plate and band joists caulked. Retro fitting a basement that wasn't done right will be tougher, especially if it is finished. You have 2 sources of moisture, coming in through the floor and walls from the ground and warm, moist air from outside hitting the surfaces cooled by the ground. Do whatever you can to seal both out.
Likely it violates code, but the only ventilation I have in the crawl space is the vent I had to add for the furnace to draw right. Another code violation, I close the damper to it in the summer. I also have the walls insulated. The crawl space is dry year around, warm in winter, and cool in the summer. I also have the floor above caulked and sealed. In the winter, warm, moist air can't follow the plumbing and wiring to the attic and condense there.